NAME DATE PERIOD. 11. Is the relation (year, percent of women) a function? Explain. Yes; each year is

(1)

Functions

Determine whether each relation is a function. Explain.

1. {(4, 5), (0, 9), (1, 0), (7, 0)}

Yes; each x value is paired with

only one y value.

3. {(2, 3), (6, 8), (4, 2), (6, 5), (2, 5)}

No; 6 in the domain is paired with

8 and 5 in the range.

5. No; 5 in the domain is paired

with 1 and 0 in the range.

7. No; 3.0 in the domain is paired

with 4.2 and 3.7 in the range.

2. {(5, 12), (1, 2), (8, 5), (4, 2), (3, 5)}

Yes; each x value is paired with

only one y value.

4. {(5, 2), ( 2, 15), (7, 15), (1, 5), (4, 15), (7, 2)}

No; 7 in the domain is paired

with 15 and 2 in the range.

6. Yes; each x value is paired with

only one y value.

8. No; 4 in the domain is paired with

2 and 2 in the range.

EMPLOYMENT For Exercises 9–12, use the

table, which shows the percent of employed

men and women in the U.S. labor force

every five years from 1980 to 2000.

9. Is the relation (year, percent of men) a

function? Explain. Yes; each year is

paired with only one value for the

percent of employed men.

10. Describe how the percent of employed

men is related to the year. The number

of employed men varies each year,

but is around 76 percent of the

male population.

11. Is the relation (year, percent of women) a function? Explain. Yes; each year is

paired with only one value for the percent of employed women.

12. Describe how the percent of employed women is related to the year. As the years

progress, the percent of employed women increases.

Employed Members of Labor Force

Year

Men Women

(% of male (% of female

population) population)

1980 77.4 51.5

1985 76.3 54.5

1990 76.4 57.5

1995 75.0 58.9

2000 78.9 67.3

Source: U.S. Census Bureau

Lesson 8-1

x 4 5 11 5 23

y 3 1 1 0 6

x

y

x 7 14 11 10 1

y 3 9 4 3 15

x

y

x 3.0 3.5 4.1 3.0 3.4

y 4.2 3.7 3.8 3.7 4.0

x

y

x 11 4 2 4 7

y 7 2 2 2 6

x

y

(2)

©

Glencoe/McGraw-Hill 424 Glencoe Pre-Algebra

Practice

Linear Equations in Two Variables

NAME ______________________________________ DATE PERIOD _

8-2 8-2

Find four solutions of each equation. Write the solutions as ordered pairs.

1–6. Sample answers are given.

1. y x 5 2. y 7 3. y 3x 1

( 1, 6), (0, 5), ( 1, 7), (0, 7), ( 1, 4), (0, 1),

(1, 4), (2, 3) (1, 7), (2, 7) (1, 2), (2, 5)

4. x y 6 5. y 2x 4 6. 7x y 14

( 1, 7), (0, 6), ( 1, 2), (0, 4), ( 1, 21), (0, 14),

(1, 5), (2, 4) (1, 6), (2, 8) (1, 7), (2, 0)

Graph each equation by plotting ordered pairs.

7. y 2x 1 8. y 6x 2 9. y x 4

10. y 7 11. y 3x 9 12. y 1

2 x 6

COOKING For Exercises 13–15, use the following information.

Kirsten is making gingerbread cookies using her grandmother’s recipe and needs to convert

grams to ounces. The equation y 0.04x describes the approximate

number of ounces y in x grams.

13. Find three ordered pairs of values that satisfy this equation.

Sample answer: (100, 4), (200, 8), (300, 12)

14. Draw the graph that contains these points.

15. Do negative values of x make sense in this case? Explain.

No; a recipe cannot contain a negative number

of grams of an ingredient.

y

¹₂

x – 6

x

y

2

4

6

8

4

6

8

2 4 6 8

O

2

4

8

6

2 y 3x – 9

x

y

2

4

6

8

4

6

2

4

6

8

10 4 6 8

2 y 7 O

x

y

2

4

6

8

4

6

8

10

2

4

6 4 6 8

2 O

y x + 4

x

y

O

y 6x + 2

x

y

2

4

6

8

2

4

6

2

4

6

8

10 4 6 8

2 O

y 2x – 1

x

y

O

x

8 y

2

1

3

4

5

6

7 100 200 300 400

O

Grams

Ounces

(3)

Graphing Linear Equations Using Intercepts

Find the x-intercept and the y-intercept for the graph of each equation.

1. y 2x 2 2. y 4 0 3. y 3x 9

1, 2 none, 4 3, 9

4. 6x 12y 24 5. 5x 3y 15 6. x 7 0

4, 2 3, 5 7, none

Graph each equation using the x- and y-intercepts.

7. y x 7 8. y x 5 9. y 2x 4

10. y 1

7 x 1 11. 5x 2y 10 12. x 2

13. SAVINGS Rashid’s grandparents started a savings

account for him, contributing $1000. He deposits $430

each month into the account. The equation y 430x

1000 represents how much money is in the savings

account after x number of months. Graph the equation

and explain what the y-intercept means.

The y-intercept 1000 shows how much money

was in the savings account before Rashid made

any deposits.

(2, 0)

x 2

x

y

O

(2, 0)

(0, 5) y –

⁵

x + 5

2

x

y

4

6

8

2

4 2 6 8

O

4

2

6

8 4 2

6

8 (0, 1)

y –

¹

x – 1

7

( 7, 0)

x

y

6

4

8

2

6

4 2 8

O

2

4

6

8 6 4 2

8 (0, 4)

(2, 0)

y 2x – 4

x

y

O

(5, 0)

y x + 5

(0, 5)

x

y

4

6

8

2

4 2 6 8

O

2

4

6

8

4

6 8 2

(7, 0)

y x 7

(0, 7)

x

y

2

4

6

8

4

6

8

2

4

6

8 4 6 8

2 O

y 430x 1000

2

4

6

8

10

12

14

16

18 5 1 0 1 5 2 0

Months

$ (thousand)

O

y

x

Lesson 8-3

(4)

©

Glencoe/McGraw-Hill 434 Glencoe Pre-Algebra

Practice

Slope

NAME ______________________________________ DATE PERIOD _

8-4 8-4

Find the slope of each line.

1. 2. 3.

4 ²

3 5

Find the slope of the line that passes through each pair of points.

4. A(10, 6), B(5, 8) 5. C(7, 3), D(11, 4) 6. E(5, 2), F(12, 3)

2 5 1

4 5

7 7. G(15, 7), H(10, 6) 8. J(13, 0), K(3, 12) 9. L(5, 3), M(4, 9)

1 5 3

4 6

10. P(12, 2), Q(18, 2) 11. R(2, 3), S(2, 5) 12. T(13, 8), U(21, 8)

2 3 undefined 0

13. CAKES A wedding cake measures 2 feet high in the center and the diameter of the

bottom tier is 12 inches. What is the slope of the cake? 4

14. INSECTS One particularly large ant hill found in 1997 measured 40 inches wide at

the base and 18 inches high. What was the slope of the ant hill?

1

9

0 15. ARCHAEOLOGY Today, the Great Pyramid at Giza near Cairo, Egypt, stands 137

meters tall, coming to a point. Its base is a square with each side measuring 230 meters

wide. What is the slope of the pyramid?

1

3

1

7

5 16. BUSINESS One warehouse uses 8-foot long ramps to load its forklifts onto the flat

beds of trucks for hauling. If the bed of a truck is 2 feet above the ground and the ramp

is secured to the truck at its end, what is the slope of the ramp while in operation?

1

4 x

y

4 2 6 8

O

4

6

8

4

6

8

4

2 (2, 6)

(0, 4)

x

y

O

(3, 1)

(0, 3)

x

y

O

(0, 2)

(1, 2)

(5)

Rate of Change

Find the rate of change for each linear function.

1. 2.

decrease of 2 psi/min increase of 102 km/h

Suppose y varies directly with x. Write an equation relating x and y.

3. y 6 when x 2 4. y 27 when x 9 5. y 4 when x 16

y 3x y 3x y 1

4 x

6. y 10 when x 2 7. y 42 when x 7 8. y 3 when x 36

y 5x y 6x y

1

1 2 x

9. y 4.5 when x 9 10. y 11 when x 33 11. y 25 when x 5

y 0.5x y 1

3 x y 5x

12. y 63 when x 7 13. y 48 when x 4 14. y 26 when x 13

y 9x y 12x y 2x

TRAFFIC MANAGEMENT For Exercises 15 and 16, use the following information.

San Diego reserves express lanes on the freeways for the use of

carpoolers. In order to increase traffic flow during rush hours, other

drivers may use the express lanes for a fee. The toll varies directly

with the number of cars on the road. The table shows a sample of

possible tolls.

15. Write an equation that relates the toll x and traffic volume y.

y 521x

16. Predict the number of vehicles at a peak time if the toll

increases to $6.00. 3126 vehicles/h

17. OFFICE SUPPLIES The cost of paper varies directly with the number of reams of

paper purchased. If 2 reams cost $9.60, find the cost of 41 reams. $196.80

10

20

30

40

50 5 1 0 1 5 2 0 2 5

Time (min)

Air in Tir es (psi)

0 Toll Traffic Volume

($) (vehicles/h)

1.00 521

2.00 1042

3.00 1563

4.00 2084

Lesson 8-5

Time Distance

(h) (km)

x y

0 0

5 510

10 1020

15 1530

(6)

©

Glencoe/McGraw-Hill 444 Glencoe Pre-Algebra

Practice

Slope-Intercept Form

NAME ______________________________________ DATE PERIOD _

8-6 8-6

Given the slope and y-intercept, graph each line.

1. slope 3

4 , 2. slope 5

6 , 3. slope 1,

y-intercept 3 y-intercept 1 y-intercept 5

Graph each equation using the slope and y-intercept.

4. y 1

2 x 4 5. y x 4 6. y 6x 3

EXERCISE For Exercises 7 and 8, use the following information.

A person weighing 150 pounds burns about 320 Calories per hour walking at a moderate

pace. Suppose that the same person burns an average of 1500 Calories per day through

basic activities. The total Calories y burned by that person can be represented by the

equation y 320x 1500, where x represents the number of hours spent walking.

7. Graph the equation using the

slope and y-intercept.

y 320x 1500

1

2

4

5

3

1 2 3 4 5 6 7 8 9 1 0

Time Walking (h)

Calories Bur ned (thousands)

O

y 6x 3

x

y

O

y x 4

x

y

O

y

¹

x 4

2

x

y

O

y x 5

x

y

O

y

⁵₆

x + 1

x

y

4

6

8

4

6

8

2

4 2 6 8

O

2

4

6

8

2 y

³

x 3

4

x

y

O

8. State the slope and y-intercept of the

graph of the equation and describe what

they represent. The y-intercept

1500 represents the number of

Calories burned without exercis-

ing. The slope 320 represents the

number of Calories burned per

hour when walking.

(7)

Writing Linear Functions

Write an equation in slope-intercept form for each line.

1. slope 3, 2. slope 0,

y-intercept 2 y 3x 2 y-intercept 7 y 7

3. 4.

Write an equation in slope-intercept form for the line passing through each

pair of points.

5. (9, 0) and (6, 1) 6. (8, 6) and ( 8, 2) 7. (7, 5) and (4, 5)

y 1

3 x 3 y 1

4 x 4 y 5

8. (2, 7) and (1, 4) 9. (4, 4) and (8, 10) 10. (0, 2) and (3, 14)

y x 5 y 1

2 x 6 y 4x 2

BUSINESS For Exercises 11 and 12, use the following information.

Flourishing Flowers charges $125 plus $60 for each standard floral arrangement to deliver

and set up flowers for a banquet.

11. Write an equation in slope-intercept form that shows the cost y for flowers for x number

of arrangements. y 60x 125

12. Find the cost of providing 20 floral arrangements. $1325

INSULATION For Exercises 13 and 14, use the following information.

Renata González wants to increase the energy efficiency of her

house by adding to the insulation previously installed. The better

a material protects against heat loss, the higher its R-value, or

resistance to heat flow. The table shows the R-value of fiberglass

blanket insulation per inch of thickness. The existing insulation

in Renata’s attic has an R-value of 10.

13. Write an equation in slope-intercept form that shows the

total R-value y in the attic if she adds x number of inches

of additional insulation. y 3.2x 10

14. Estimate the total R-value in the attic if she adds 6 inches of insulation. 29.2

x

y

O

x

y

O

Lesson 8-7

y 4

3 x 3 y 3x

R-value Thickness

(in.)

0.0 0

3.2 1

6.4 2

9.6 3

Source: Oak Ridge National Laboratory

(8)

©Glencoe/McGraw-Hill 420 Glencoe Pre-Algebra

R eading to Learn Mathematics

Functions

NAME ______________________________________________ DATE ____________ PERIOD _____

8-1 8-1

How can the relationship between actual temperatures and windchill temperatures be a function?

Do the activity at the top of page 369 in your textbook. Write your answers below.

a. On grid paper, graph the temperatures as ordered pairs (actual, windchill).

b. Describe the relationship between the two temperature scales.

Sample answer:

As the actual temperature increases,

the windchill temperature also

increases.

c. When the actual temperature is 220°F, which is the best estimate for the windchill:246°F,228°F, or 0°F? Explain.

46°F; when the

actual temperature decreases, the windchill temperature

also decreases.

Pre-Activity

Reading the Lesson 1–2. See students’ work.

Write a definition and give an example of each new vocabulary word or phrase.

3. For a relation to be a function, each element in the

domain

must have only one corresponding element in the

range

.

4. Explain what is meant by the phrase “distance is a function of time.”

Sample answer:

How far something travels depends on how much time elapses.

Helping You Remember

5. You have learned various ways to determine whether a relation is a function. Choose which method is the easiest for you to use, then write a few sentences explaining how that method relates to the other methods.

Sample answer: Placing the range

values in a table with their corresponding domain values makes it easy

to see whether an element in the domain is paired with only one element

in the range. By graphing and connecting the points, the vertical line test

can be applied to arrive at the same answer.

Vocabulary Definition Example

1. function

2.vertical line test

5

5 10 15 20 25 30 35

15 5 5 15

y x O

Practice

Functions

NAME ______________________________________________ DATE ____________ PERIOD _____

8-1 8-1

Determine whether each relation is a function. Explain.

1. {(4,25), (0,29), (1, 0), (7, 0)}

Yes; each x value is paired with

only one y value.

3. {(22,23), (6,28), (4, 2), (6,25), (2,25)}

No; 6 in the domain is paired with

8 and 5 in the range.

5.

No; 5 in the domain is paired

with 1 and 0 in the range.

7.

No; 3.0 in the domain is paired

with 4.2 and 3.7 in the range.

2. {(5,212), (21,22), (8,25), (4,22), (3,25)}

Yes; each x value is paired with

only one y value.

4. {(5, 2), (22, 15), (27, 15), (1, 5), (4, 15), (27, 2)}

No; 7 in the domain is paired

with 15 and 2 in the range.

6.

Yes; each x value is paired with

only one y value.

8.

No; 4 in the domain is paired with

2 and 2 in the range.

EMPLOYMENT For Exercises 9–12, use the table, which shows the percent of employed men and women in the U.S. labor force every five years from 1980 to 2000.

9. Is the relation (year, percent of men) a function? Explain.

Yes; each year is

paired with only one value for the

percent of employed men.

10. Describe how the percent of employed men is related to the year.

The number

of employed men varies each year,

but is around 76 percent of the

male population.

11. Is the relation (year, percent of women) a function? Explain.

Yes; each year is

paired with only one value for the percent of employed women.

12. Describe how the percent of employed women is related to the year.

As the years

progress, the percent of employed women increases.

Employed Members of Labor Force

Year

Men Women

(% of male (% of female population) population)

1980 77.4 51.5

1985 76.3 54.5

1990 76.4 57.5

1995 75.0 58.9

2000 78.9 67.3

Source: U.S. Census Bureau

Lesson 8-1

x 4 5 11 5 23

y 3 1 1 0 6

x y

x 7 14 11 10 1

y 3 9 4 3 15

x y

x 3.0 3.5 4.1 3.0 3.4 y 4.2 3.7 3.8 3.7 4.0

x y

x 11 4 2 4 7

y 7 2 2 2 6

x y

©

Glencoe/McGraw-Hill A3 Glencoe Pre-Algebr a Ans wer s (Lesson 8-1)

Answers

(9)

©Glencoe/McGraw-Hill 424 Glencoe Pre-Algebra Find four solutions of each equation. Write the solutions as ordered pairs.

1–6. Sample answers are given.

1. y5x25 2. y 5 27 3. y5 23x11

( 1, 6), (0, 5), ( 1, 7), (0, 7), ( 1, 4), (0, 1),

(1, 4), (2, 3) (1, 7), (2, 7) (1, 2), (2, 5)

4. x2y56 5. y 52x1 4 6. 7x2y514

( 1, 7), (0, 6), ( 1, 2), (0, 4), ( 1, 21), (0, 14),

(1, 5), (2, 4) (1, 6), (2, 8) (1, 7), (2, 0)

Graph each equation by plotting ordered pairs.

7. y5 2x 21 8. y5 26x12 9. y5x1 4

10. y57 11. y5 3x29 12. y5}1

2}x2 6

COOKING For Exercises 13–15, use the following information.

Kirsten is making gingerbread cookies using her grandmother’s recipe and needs to convert grams to ounces. The equation y50.04x describes the approximate

number of ounces y in x grams.

13. Find three ordered pairs of values that satisfy this equation.

Sample answer: (100, 4), (200, 8), (300, 12)

14. Draw the graph that contains these points.

15. Do negative values of x make sense in this case? Explain.

No; a recipe cannot contain a negative number

of grams of an ingredient.

x y

2 4 6 8

4 6 8

2 4 6 8 O 2 4

8 6 2

y ¹₂x – 6 x

y

2 4 6 8

4 6

2

2 4 6 8 10

4 6 8 2

O

y 3x – 9 x

y

2 4 6 8

4 6 8 10

2

2 4 6

4 6 8 2

O y 7

x y

O y 5 x + 4

x y

2 4 6 8

2 4 6

2 4 6 8 10

4 6 8 2

O y 6x + 2

x y

O y 2x – 1

x 8y

2 1 3 4 5 6 7

100 200 300 400 O

Grams

Ounces

Find four solutions of each equation. Write the solutions as ordered pairs.

1–9. Sample answers are given.

1. y = 8x24 2. y 5 2x112 3. 4x24y5 24

( 1, 12), (0, 4), ( 1, 13), (0, 12), ( 1, 7), (0, 6),

(1, 4), (2, 12) (1, 11), (2, 10) (1, 5), (2, 4)

4. x2y5 215 5. y 57x2 6 6. y5 23x18

( 1, 14), (0, 15), ( 1, 13), (0, 6), ( 1, 11), (0, 8),

(1, 16), (2, 17) (1, 1), (2, 8) (1, 5), (2, 2)

7. y512 8. 4x22y 50 9. 4x2y54

( 1, 12), (0, 12), ( 1, 2), (0, 0), ( 1, 8), (0, 4),

(1, 12), (2, 12) (1, 2), (2, 4) (1, 0), (2, 4)

Graph each equation by plotting ordered pairs.

10. y53x 2 2 11. y5 2x13 12. y5 2 }1

2}x 1 }3 2}

13. y5 22 x25 14. y54x 28 15. y5}2

3}x 22

16. y5 25x 17. y5 22x16 18. y55x1 1

y 5x + 1 x y

O x

y

2 4 6 8

4 6 8

2

2 4 6 8

4 6 8 2

O y 2x + 6

x y

O y 5x

x y

O y 5²₃ x – 2 x

y

4 6 8

4 6

2

2 4 6 8 10

4

2 6 8

2 O

y 4x 8 x

y

O

y 2x 5

x y

O y ¹₂x +³₂

x y

O y x + 3

x y

O y 3x 2

Lesson 8-2

A5 Glencoe Pre-Algebr a Ans wer s (Lesson 8-2)

(10)

R eading to Learn Mathematics

Graphing Linear Equations Using Intercepts

NAME ______________________________________________ DATE ____________ PERIOD _____

8-3 8-3

How can intercepts be used to represent real-life information?

a. Write the ordered pair for the point where the graph intersects the y-axis. What does this point represent?

(0, 32); a temperature of

0°C equals 32°F.

b. Write the ordered pair for the point where the graph intersects the x-axis. What does this point represent?

( 18, 0); a temperature

of approximately 18°C equals 0°F.

Pre-Activity

Reading the Lesson 1–2. See students’ work.

Write a definition and give an example of each new vocabulary word.

3. The y-coordinate of the x-intercept is 0.

The x-coordinate of the y-intercept is 0.

4. Draw a model on the coordinate grid that shows how to graph a line using the x-intercept and the y-intercept of a line. Explain your model.

5. Is a line with no x-intercept vertical or horizontal? Explain.

Horizontal; if a line has

no x-intercept, the line will never cross the x-axis. Therefore, the line

must be parallel to the x-axis.

Helping You Remember

6. The word intercept has many synonyms in English. Look up intercept in a thesaurus and find one or two synonyms that help you remember the mathematical meaning of the word.

Explain your selection.

Sample answer: cut off; The y-intercept is where the

y-axis cuts off the line; the x-intercept is where the x-axis cuts off the line.

(5, 0) (0, 3)

x y

O 2 24 26 28

6 8

2 4

22 24 26 28

4 6 8 22

x-intercept

y-intercept

Sample answer: The x-intercept is 5, which means

that one point of the graph is at (5, 0). The y-inter-

cept is 3, which means that another point of the

graph is at (0, 3). Graph both points on the grid and

draw a line through them.

1.

2.

Practice

Graphing Linear Equations Using Intercepts

NAME ______________________________________________ DATE ____________ PERIOD _____

8-3 8-3

Find the x-intercept and the y-intercept for the graph of each equation.

1. y52x22 2. y14 50 3. y5 3x19

1, 2 none, 4 3, 9

4. 6x1 12y524 5. 5x2 3y515 6.2x27 50

4, 2 3, 5 7, none

Graph each equation using the x- and y-intercepts.

7. y5x27 8. y5 2x1 5 9. y 5 2x24

10. y5 2}1

7}x2 1 11. 5x1 2y510 12. x52

13.SAVINGS Rashid’s grandparents started a savings account for him, contributing $1000. He deposits $430 each month into the account. The equation y5430x1 1000 represents how much money is in the savings account after x number of months. Graph the equation and explain what the y-intercept means.

The y-intercept 1000 shows how much money

was in the savings account before Rashid made

any deposits.

x y

O x 5 2 (2, 0) x

y 4 6 8

2 4

2 6 8

O

24 22 26 28 2422 26 28

y 5 –⁵₂x + 5 (2, 0) (0, 5)

x y 6 4 8

2 6 4

2 8

O 2 4 6 8 6 4 2 8

y –¹x – 1 7 ( 7, 0)

(0, 1)

x y

O

y 2x – 4 (0, 4)

(2, 0) x

y 4 6 8

2 4

2 68

O 22 24 26 28 24 26

28 22

y 5 2x + 5 (0, 5)

(5, 0) x

y

2 24 26 28

4 6 8

2

22 24 26 28

4 6 8 22

O y 5 x 2 7

(0, 27) (7, 0)

2 4 6 8 10 12 14 16 18

5 1 0 1 5 2 0 Months

$ (thousand)

O

y 430x 1000 y

x

Lesson 8-3

©

Glencoe/McGraw-Hill A8 Glencoe Pre-Algebr a Ans wer s (Lesson 8-3)

(11)

1. 2. 3.

4

}2

3}

5

Find the slope of the line that passes through each pair of points.

4. A(210, 6), B(25, 8) 5. C(7,23), D(11,24) 6. E(5, 2), F(12,23) }2

5} }1

4} }5

7}

7. G(215, 7), H(210, 6) 8. J(13, 0), K(23,212) 9. L(25, 3), M(24, 9) }1

5} }3

4}

6

10. P(12, 2), Q(18,22) 11. R(22,23), S(22,25) 12. T(213, 8), U(21, 8) }2

3}

undefined 0

13.CAKES A wedding cake measures 2 feet high in the center and the diameter of the bottom tier is 12 inches. What is the slope of the cake?

4

14.INSECTS One particularly large ant hill found in 1997 measured 40 inches wide at the base and 18 inches high. What was the slope of the ant hill?

}1 9

0}

15.ARCHAEOLOGY Today, the Great Pyramid at Giza near Cairo, Egypt, stands 137 meters tall, coming to a point. Its base is a square with each side measuring 230 meters wide. What is the slope of the pyramid?

}1 1 3 1 7 }5

16.BUSINESS One warehouse uses 8-foot long ramps to load its forklifts onto the flat beds of trucks for hauling. If the bed of a truck is 2 feet above the ground and the ramp is secured to the truck at its end, what is the slope of the ramp while in operation?

}1 4}

x y

4

2 6 8

O 4 6 8 4 6 8

4 2

(2, 6) (0, 4)

x y

O

(3, 1)

(0, 3) x

y

O (0, 2)

(1, 2)

Find the slope of each line.

1. 2. 3.

}1

4}

2 5

4. 5. 6.

4

^}¹

2}

6

Find the slope of the line that passes through each pair of points.

7. A(1,25), B(6,27) 8. C(7,23), D(8, 1) 9. E(7, 2), F(12, 6) }2

5}

4

}4

5}

10. G(8,23), H(11,22) 11. J(5,29), K(0,212) 12. L(24, 6), M(5, 3) }1

3} }3

5} }1

3}

13. P(2,22), Q(7,21) 14. R(25,22), S(25, 3) 15. T(5,26), U(8,212) }1

5}

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16. P(10,22), Q(3,21) 17. R(6,25), S(7, 3) 18. T(1, 8), U(7, 8) }1

7}

8 0

19.CAMPING A family camping in a national forest builds a temporary shelter with a tarp and a 4-foot pole. The bottom of the pole is even with the ground, and one corner is staked 5 feet from the bottom of the pole. What is the slope of the tarp from that corner to the top of the pole?

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20.ART A rectangular painting on a gallery wall measures 7 meters high and 4 meters wide. What is the slope from the upper left corner to the lower right corner?

}7 4}

x y

O (0, 2)

(1, 4)

x y

O (0, 3)

(4, 1)

x y

O

(1, 3) (0, 1)

x y

O (0, 1)

(1, 4)

x y

O (0, 3)

(2, 1) x

y

O (0, 2)

(4, 3)

Lesson 8-4

A10 Glencoe Pre-Algebr a Ans wer s (Lesson 8-4)

(12)

R eading to Learn Mathematics

Rate of Change

NAME ______________________________________________ DATE ____________ PERIOD _____

8-5 8-5

How are slope and speed related?

a. For every 1-hour increase in time, what is the change in distance?

55 mi

b. Find the slope of the line.

55

c. Make a conjecture about the relationship between slope of the line and speed of the car.

Slope is equal to the speed of the car.

Pre-Activity

Reading the Lesson 1–3. See students’ work.

Write a definition and give an example of each new vocabulary phrase.

Complete each sentence.

4. Rates of change can be described using

slope

. 5. Direct variation is a special type of

linear

equation.

Helping You Remember

6. The word ratio comes from the Latin word meaning rate and can also mean proportion or relation. Direct variation is often called direct proportion. Look up ratio in the dictionary. Then use this information to explain the relationship between rate of change and direct variation.

Sample answers: The rate of change is the ratio of the

change in one quantity to the change in another quantity. If the ratio is

direct, or proportional, then both quantities vary at the same,

or constant, rate. Either they both increase at the same rate or they both

decrease at the same rate.

1. rate of change 2. direct

variation 3. constant of

variation

Practice

Rate of Change

NAME ______________________________________________ DATE ____________ PERIOD _____

8-5 8-5

Find the rate of change for each linear function.

1. 2.

decrease of 2 psi/min increase of 102 km/h

Suppose y varies directly with x. Write an equation relating x and y.

3. y5 26 when x5 22 4. y5 227 when x59 5. y54 when x516

y

3x

y

3x

y ^}¹

4}x 6. y510 when x52 7. y5 242 when x57 8. y5 3 when x536

y

5x

y

6x

y }

1 1

2}x

9. y54.5 when x5 29 10. y511 when x533 11. y5 25 when x5 25

y

0.5x

y }1

3}x y

5x

12. y563 when x57 13. y548 when x5 24 14. y5 26 when x5 13

y

9x

y

12x

y

2x

TRAFFIC MANAGEMENT For Exercises 15 and 16, use the following information.

San Diego reserves express lanes on the freeways for the use of carpoolers. In order to increase traffic flow during rush hours, other drivers may use the express lanes for a fee. The toll varies directly with the number of cars on the road. The table shows a sample of possible tolls.

15. Write an equation that relates the toll x and traffic volume y.

y

521x

16. Predict the number of vehicles at a peak time if the toll increases to $6.00.

3126 vehicles/h

17.OFFICE SUPPLIES The cost of paper varies directly with the number of reams of paper purchased. If 2 reams cost $9.60, find the cost of 41 reams.

$196.80

10 20 30 40 50

5 1 0 1 5 2 0 2 5 Time (min)

Air in Tires (psi)

0

Toll Traffic Volume ($) (vehicles/h)

1.00 521

2.00 1042

3.00 1563

4.00 2084

Lesson 8-5

Time Distance (h) (km)

x y

0 0

5 510

10 1020

15 1530

©

Glencoe/McGraw-Hill A13 Glencoe Pre-Algebr a Ans wer s (Lesson 8-5)

Answers

(13)

1. slope 5}3

4}, 2. slope 5}5

6}, 3. slope 51,

y-intercept 5 23 y-intercept 51 y-intercept 55

Graph each equation using the slope and y-intercept.

4. y5 2}1

2}x24 5. y5x24 6. y5 26x13

EXERCISE For Exercises 7 and 8, use the following information.

A person weighing 150 pounds burns about 320 Calories per hour walking at a moderate pace. Suppose that the same person burns an average of 1500 Calories per day through basic activities. The total Calories y burned by that person can be represented by the equation y5320x1 1500, where x represents the number of hours spent walking.

7. Graph the equation using the slope and y-intercept.

1 2 4 5

3

1

2 3 4 5 6 7 8 9 1 0 Time Walking (h) Calories Burned (thousands)

O

y 320x 1500

x y

O y 6x 3

x y

O

y x 4 x

y

O y ¹₂x 4

x y

O y x 5 x

y

4 6 8

2 4

2 6 8

O 2 4 6 8 2 y ⁵₆x + 1 x

y

O

y ³₄x 3

8. State the slope and y-intercept of the graph of the equation and describe what they represent.

The y-intercept

1500 represents the number of

Calories burned without exercis-

ing. The slope 320 represents the

number of Calories burned per

hour when walking.

State the slope and the y-intercept for the graph of each equation.

1. y512x24 2. y5}1

4}x13 3. 3x2y56

12; 4

^}¹

4}

; 3 3; 6

Given the slope and y-intercept, graph each line.

4. slope 5 22, 5. slope 5}1

2}, 6. slope 5}2

3},

y-intercept 52 y-intercept 54 y-intercept 5 23

Graph each equation using the slope and y-intercept.

7. y55x2 1 8. y5}1

2}x14 9. y5 2x12

10. y52x1 2 11. y5 24x12 12. y5 x23

x y

O y x 3

x y

O y 4x 2

x y

O y 2x 2

x y

O y x 2

x y

O y ¹₂x + 4

x y

O y 5x 1

x y

O

y ²₃x 3 x

y

O y ¹₂x + 4

x y

O y 2x 2

Lesson 8-6

A15 Glencoe Pre-Algebr a Ans wer s (Lesson 8-6)

(14)

R eading to Learn Mathematics

Writing Linear Functions

NAME ______________________________________________ DATE ____________ PERIOD _____

8-7 8-7

How can you model data with a linear equation?

a. Graph the ordered pairs (chirps, temperature). Draw a line through the points.

b. Find the slope and the y-intercept of the line. What do these values represent?

Slope 1 represents the rate of change, 1

degree for every 1 chirp; y-intercept 40 represents the

temperature at which the crickets are not chirping.

c. Write an equation in the form y5mx1b for the line then translate the equation into a sentence. y x

40; The temperature

equals the number of chirps in 15 seconds plus 40.

Pre-Activity

Reading the Lesson

1. Explain how you can use the following information to write the slope-intercept form of a line.

a. graph of a line

Find the y-intercept. From that point, count how many

units up or down and how many units left or right to another point. The

slope is the ratio of the rise over the run. Then substitute the slope

and the y-intercept into the slope-intercept form.

b. two points on a line

Substitute the coordinates of two points on the

line into the definition of slope. Then use the slope and one of the

points to find the y-intercept. Substitute the slope and the point’s

coordinates into slope-intercept form. Then substitute the slope and

the y-intercept into the slope-intercept form.

c. a table of values

Use the table to identify the coordinates of two points

on the line. Then substitute the coordinates of the two points on the

line into the definition of slope. Then use the slope and one of the

points to find the y-intercept. Substitute the slope and the point’s

coordinates into slope-intercept form. Then substitute the slope and

the y-intercept into the slope-intercept form.

Temperature (˚F) 30

10

0 50 70

40

20 60

Number of Chirps 10 15 20 25 30 35 5

y

x

Practice

Writing Linear Functions

NAME ______________________________________________ DATE ____________ PERIOD _____

8-7 8-7

Write an equation in slope-intercept form for each line.

1. slope 53, 2. slope 50,

y-intercept 5 22 y

3x 2

y-intercept 5 7 y

7

3. 4.

Write an equation in slope-intercept form for the line passing through each pair of points.

5. (9, 0) and (6,21) 6. (8, 6) and (28, 2) 7. (7,25) and (24,25) y ^}¹

3}x

3

y ^}¹

4}x

4

y

5

8. (2, 7) and (21, 4) 9. (4, 4) and (28, 10) 10. (0, 2) and (23, 14)

y x

5

y }1

2}x

6

y

4x 2

BUSINESS For Exercises 11 and 12, use the following information.

Flourishing Flowers charges $125 plus $60 for each standard floral arrangement to deliver and set up flowers for a banquet.

11. Write an equation in slope-intercept form that shows the cost y for flowers for x number of arrangements. y

60x 125

12. Find the cost of providing 20 floral arrangements.

$1325

INSULATION For Exercises 13 and 14, use the following information.

Renata González wants to increase the energy efficiency of her house by adding to the insulation previously installed. The better a material protects against heat loss, the higher its R-value, or resistance to heat flow. The table shows the R-value of fiberglass blanket insulation per inch of thickness. The existing insulation in Renata’s attic has an R-value of 10.

13. Write an equation in slope-intercept form that shows the total R-value y in the attic if she adds x number of inches of additional insulation. y

3.2x 10

14. Estimate the total R-value in the attic if she adds 6 inches of insulation.

29.2

x y

O x

y

O

Lesson 8-7

y ^}⁴

3}x

3

y

3x

R-value Thickness (in.)

0.0 0

3.2 1

6.4 2

9.6 3

Source: Oak Ridge National Laboratory

©